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Activation functions play a significant role in neural network design by enabling non-linearity. The choice of activation function was previously shown to influence the properties of the resulting loss landscape. Understanding the relationship between activation functions and loss landscape properties is important for neural architecture and training algorithm design. This study empirically investigates neural network loss landscapes associated with hyperbolic tangent, rectified linear unit, and exponential linear unit activation functions. Rectified linear unit is shown to yield the most convex loss landscape, and exponential linear unit is shown to yield the least flat loss landscape, and to exhibit superior generalisation performance. The presence of wide and narrow valleys in the loss landscape is established for all activation functions, and the narrow valleys are shown to correlate with saturated neurons and implicitly regularised network configurations.

Physics-informed neural networks (PINNs) have recently emerged as promising data-driven PDE solvers showing encouraging results on various PDEs. However, there is a fundamental limitation of training PINNs to solve multi-dimensional PDEs and approximate highly complex solution functions. The number of training points (collocation points) required on these challenging PDEs grows substantially, but it is severely limited due to the expensive computational costs and heavy memory overhead. To overcome this issue, we propose a network architecture and training algorithm for PINNs. The proposed method, separable PINN (SPINN), operates on a per-axis basis to significantly reduce the number of network propagations in multi-dimensional PDEs unlike point-wise processing in conventional PINNs. We also propose using forward-mode automatic differentiation to reduce the computational cost of computing PDE residuals, enabling a large number of collocation points (>10^7) on a single commodity GPU. The experimental results show drastically reduced computational costs (62x in wall-clock time, 1,394x in FLOPs given the same number of collocation points) in multi-dimensional PDEs while achieving better accuracy. Furthermore, we present that SPINN can solve a chaotic (2+1)-d Navier-Stokes equation significantly faster than the best-performing prior method (9 minutes vs 10 hours in a single GPU), maintaining accuracy. Finally, we showcase that SPINN can accurately obtain the solution of a highly nonlinear and multi-dimensional PDE, a (3+1)-d Navier-Stokes equation.

For many decades, advances in static verification have focused on linear integer arithmetic (LIA) programs. Many real-world programs are, however, written with non-linear integer arithmetic (NLA) expressions, such as programs that model physical events, control systems, or nonlinear activation functions in neural networks. While there are some approaches to reasoning about such NLA programs, still many verification tools fall short when trying to analyze them. To expand the scope of existing tools, we introduce a new method of converting programs with NLA expressions into semantically equivalent LIA programs via a technique we call dual rewriting. Dual rewriting discovers a linear replacement for an NLA Boolean expression (e.g. as found in conditional branching), simultaneously exploring both the positive and negative side of the condition, and using a combination of static validation and dynamic generalization of counterexamples. While perhaps surprising at first, this is often possible because the truth value of a Boolean NLA expression can be characterized in terms of a Boolean combination of linearly-described regions/intervals where the expression is true and those where it is false. The upshot is that rewriting NLA expressions to LIA expressions beforehand enables off-the-shelf LIA tools to be applied to the wider class of NLA programs. We built a new tool DrNLA and show it can discover LIA replacements for a variety of NLA programs. We then applied our work to branching-time verification of NLA programs, creating the first set of such benchmarks (92 in total) and showing that DrNLA's rewriting enable tools such as FuncTion and T2 to verify CTL properties of 42 programs that previously could not be verified. We also show a potential use of DrNLA assisting Frama-C in program slicing, and report that execution speed is not impacted much by rewriting.

As an efficient alternative to conventional full finetuning, parameter-efficient finetuning (PEFT) is becoming the prevailing method to adapt pretrained language models. In PEFT, a lightweight module is learned on each dataset while the underlying pretrained language model remains unchanged, resulting in multiple compact modules representing diverse skills when applied to various domains and tasks. In this paper, we propose to compose these parameter-efficient modules through linear arithmetic operations in the weight space, thereby integrating different module capabilities. Specifically, we first define addition and negation operators for the module, and then further compose these two basic operators to perform flexible arithmetic. Our approach requires \emph{no additional training} and enables highly flexible module composition. We apply different arithmetic operations to compose the parameter-efficient modules for (1) distribution generalization, (2) multi-tasking, (3) unlearning, and (4) domain transfer. Additionally, we extend our approach to detoxify Alpaca-LoRA, the latest instruction-tuned large language model based on LLaMA. Empirical results demonstrate that our approach produces new and effective parameter-efficient modules that significantly outperform existing ones across all settings.

There is an increasing interest in learning reward functions that model human intent and human preferences. However, many frameworks use blackbox learning methods that, while expressive, are difficult to interpret. We propose and evaluate a novel approach for learning expressive and interpretable reward functions from preferences using Differentiable Decision Trees (DDTs). Our experiments across several domains, including Cartpole, Visual Gridworld environments and Atari games, provide evidence that that the tree structure of our learned reward function is useful in determining the extent to which the reward function is aligned with human preferences. We experimentally demonstrate that using reward DDTs results in competitive performance when compared with larger capacity deep neural network reward functions. We also observe that the choice between soft and hard (argmax) output of reward DDT reveals a tension between wanting highly shaped rewards to ensure good RL performance, while also wanting simple, non-shaped rewards to afford interpretability.

Verification and safety assessment of neural network controlled systems (NNCSs) is an emerging challenge. To provide guarantees, verification tools must efficiently capture the interplay between the neural network and the physical system within the control loop. In this paper, a compositional approach focused on inclusion preserving long term symbolic dependency modeling is proposed for the analysis of NNCSs. First of all, the matrix structure of symbolic zonotopes is exploited to efficiently abstract the input/output mapping of the loop elements through (inclusion preserving) affine symbolic expressions, thus maintaining linear dependencies between interacting blocks. Then, two further extensions are studied. Firstly, symbolic polynotopes are used to abstract the loop elements behaviour by means of polynomial symbolic expressions and dependencies. Secondly, an original input partitioning algorithm takes advantage of symbol preservation to assess the sensitivity of the computed approximation to some input directions. The approach is evaluated via different numerical examples and benchmarks. A good trade-off between low conservatism and computational efficiency is obtained.

Energy is today the most critical environmental challenge. The amount of carbon emissions contributing to climate change is significantly influenced by both the production and consumption of energy. Measuring and reducing the energy consumption of services is a crucial step toward reducing adverse environmental effects caused by carbon emissions. Millions of websites rely on online advertisements to generate revenue, with most websites earning most or all of their revenues from ads. As a result, hundreds of billions of online ads are delivered daily to internet users to be rendered in their browsers. Both the delivery and rendering of each ad consume energy. This study investigates how much energy online ads use in the rendering process and offers a way for predicting it as part of rendering the ad. To the best of the authors' knowledge, this is the first study to calculate the energy usage of single advertisements in the rendering process. Our research further introduces different levels of consumption by which online ads can be classified based on energy efficiency. This classification will allow advertisers to add energy efficiency metrics and optimize campaigns towards consuming less possible.

The generalization mystery in deep learning is the following: Why do over-parameterized neural networks trained with gradient descent (GD) generalize well on real datasets even though they are capable of fitting random datasets of comparable size? Furthermore, from among all solutions that fit the training data, how does GD find one that generalizes well (when such a well-generalizing solution exists)? We argue that the answer to both questions lies in the interaction of the gradients of different examples during training. Intuitively, if the per-example gradients are well-aligned, that is, if they are coherent, then one may expect GD to be (algorithmically) stable, and hence generalize well. We formalize this argument with an easy to compute and interpretable metric for coherence, and show that the metric takes on very different values on real and random datasets for several common vision networks. The theory also explains a number of other phenomena in deep learning, such as why some examples are reliably learned earlier than others, why early stopping works, and why it is possible to learn from noisy labels. Moreover, since the theory provides a causal explanation of how GD finds a well-generalizing solution when one exists, it motivates a class of simple modifications to GD that attenuate memorization and improve generalization. Generalization in deep learning is an extremely broad phenomenon, and therefore, it requires an equally general explanation. We conclude with a survey of alternative lines of attack on this problem, and argue that the proposed approach is the most viable one on this basis.

Autonomous driving has achieved a significant milestone in research and development over the last decade. There is increasing interest in the field as the deployment of self-operating vehicles on roads promises safer and more ecologically friendly transportation systems. With the rise of computationally powerful artificial intelligence (AI) techniques, autonomous vehicles can sense their environment with high precision, make safe real-time decisions, and operate more reliably without human interventions. However, intelligent decision-making in autonomous cars is not generally understandable by humans in the current state of the art, and such deficiency hinders this technology from being socially acceptable. Hence, aside from making safe real-time decisions, the AI systems of autonomous vehicles also need to explain how these decisions are constructed in order to be regulatory compliant across many jurisdictions. Our study sheds a comprehensive light on developing explainable artificial intelligence (XAI) approaches for autonomous vehicles. In particular, we make the following contributions. First, we provide a thorough overview of the present gaps with respect to explanations in the state-of-the-art autonomous vehicle industry. We then show the taxonomy of explanations and explanation receivers in this field. Thirdly, we propose a framework for an architecture of end-to-end autonomous driving systems and justify the role of XAI in both debugging and regulating such systems. Finally, as future research directions, we provide a field guide on XAI approaches for autonomous driving that can improve operational safety and transparency towards achieving public approval by regulators, manufacturers, and all engaged stakeholders.

With the advent of deep neural networks, learning-based approaches for 3D reconstruction have gained popularity. However, unlike for images, in 3D there is no canonical representation which is both computationally and memory efficient yet allows for representing high-resolution geometry of arbitrary topology. Many of the state-of-the-art learning-based 3D reconstruction approaches can hence only represent very coarse 3D geometry or are limited to a restricted domain. In this paper, we propose occupancy networks, a new representation for learning-based 3D reconstruction methods. Occupancy networks implicitly represent the 3D surface as the continuous decision boundary of a deep neural network classifier. In contrast to existing approaches, our representation encodes a description of the 3D output at infinite resolution without excessive memory footprint. We validate that our representation can efficiently encode 3D structure and can be inferred from various kinds of input. Our experiments demonstrate competitive results, both qualitatively and quantitatively, for the challenging tasks of 3D reconstruction from single images, noisy point clouds and coarse discrete voxel grids. We believe that occupancy networks will become a useful tool in a wide variety of learning-based 3D tasks.